Syndication

Wondermark 700 raises the question of which dollar you're withdrawing when you withdraw a dollar from a bank account. Is it first-in first-out like a queue? Is it last-in first-out like a stack? One character in the strip says the question is silly and meaningless, but I'm not so sure; and I think the correct answer is neither stack nor queue.

Consider the case of a mutual fund, which is much like a bank account but it holds "units" instead of dollars, and the value of a unit in dollars fluctuates. I might buy 100 at $10 each, then later buy 100 more at $20 each, and then sell 100 at $30 each. It matters which units I sold, because that determines what my profit was; and it matters how much my profit was, because that determines how much capital gains tax I have to pay. If I'm selling the $10 units then I have a capital gain of $2000; if I'm selling the $20 units then I have a capital gain of $1000.

The legal rule (in Canada, assuming the units are classified as capital property, and of course I'm not a tax lawyer and this is not tax advice) is that when you sell you are selling a proportional share of all the units you have. In my example, if I buy 100 at $10, buy 100 at $20, then sell 100 at $30, the calculation is that I bought a total of 200 for a total of $3000. I am selling half of that pile, so the half I am selling had a total cost of $1500 and my capital gain is $1500. The remaining unsold units now have an "adjusted cost base" of $1500, which will be used when I sell them in the future. Although the tax calculation is phrased in terms of the buying and selling price of the entire pile of units, it's easy to see that under the covers what's going on is that as soon as units are added to the pile, they become uniformly and inseparably mixed with the units already there. When units are removed, they are removed proportionally from the entire pile.

And I think that's also the most reasonable way to think about dollars in a bank account. If your account has never been emptied completely, then some trace of every dollar ever deposited remains. But if your balance has fluctuated much, then some of those traces may by this time be very small indeed, because every withdrawal is coming out of every dollar in the account.

I note that something similar is also what is said to happen with souls in some spiritual contexts - in particular, it's part of the reason that it's not practicable to "de-enshrine" some of the souls of Japanese soldiers from WWII which have merged into the deities of certain Shinto shrines, however much it might no longer be politically acceptable to honour such souls. However, it's not exactly the same thing because spiritual essence in general does not dilute. If you mix one litre of holy water with one litre of ordinary water, you get two litres of holy water. There may be exceptions when the amount of dilution is extremely massive, like one drop into the ocean - there are people who claim to have blessed entire large bodies of water but I don't think that's generally accepted - or in the case of mixing with something that is unclean enough to actively negate the holiness.

The mutual fund example isn't cut-and-dried, either. Many mutual fund companies apply a first-in, first-out rule for calculating back-end load. When you sell units, you may be charged a fee called "load" that varies depending on how old the units are, with older units eligible for a smaller, or no, fee. Usually the rule is that for the purposes of calculating this fee, you are always selling the oldest units first; that's the rule most advantageous to the customer and it's arguably the most fair. On the other hand, most fund companies will also charge a "short-term trading" fee or penalty if you sell units less than 90 days (or some similar length of time) after your most recent purchase of units - even if, under the first-in first-out rule, the units you are selling include no part of the units you bought recently. The basic function of this rule seems to be to prevent you from gaming the first-in first-out rule; but it amounts to applying a last-in first-out rule. So it's possible, if you bought units a long time ago and also very recently and then sold some units, that you could have all three rules applied to the same transaction: first-in first-out for load, last-in first-out for the short-term trading penalty, and proportional representation for tax purposes.

It may be instructive to note the case of Paddington Brown, who deposited some money in an English bank and was very disappointed later when he tried to withdraw it and they tried to give him a pound note with a different serial number from the one he'd recorded when he made his deposit. And then, of course, there's also the matter of The Ghost in the Bank of England.